© Published under licence by IOP Publishing Ltd. DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consists of three drag-free spacecraft arranged in an equilateral triangle with 1000 km arm lengths whose relative displacements are measured by a differential Fabry-Perot interferometer, and four units of triangular Fabry-Perot interferometers are arranged on heliocentric orbit around the sun. DECIGO is vary ambitious mission, we plan to launch DECIGO in era of 2030s after precursor satellite mission, B-DECIGO. B-DECIGO is essentially smaller version of DECIGO: B-DECIGO consists of three spacecraft arranged in an triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be late 2020s for the present..

We study the cosmological dynamics of a D-BIonic and Dirac-Born-Infeld scalar field, which is coupled to matter fluid. For the exponential potential and the exponential couplings, we find a new analytic scaling solution yielding the accelerated expansion of the Universe. Since it is shown to be an attractor for some range of the coupling parameters, the density parameter of matter fluid can be the observed value, as in the coupled quintessence with a canonical scalar field. Contrary to the usual coupled quintessence, where the value of the matter coupling giving the observed density parameter is too large to satisfy the observational constraint from the cosmic microwave background, we show that the D-BIonic theory can give a similar solution with a much smaller value of matter coupling. As a result, together with the fact that the D-BIonic theory has a screening mechanism, the D-BIonic theory can solve the so-called coincidence problem as well as the dark energy problem.

We study the Einstein-SO(3) Yang-Mills-Higgs system with a negative cosmological constant and find the monopole black hole solutions as well as the trivial Reissner-Nordstrm black hole. We discuss thermodynamical stability of the monopole black hole in an isolated system. We expect a phase transition between those two black holes when the mass of a black hole increases or decreases. The type of phase transition depends on the cosmological constant Lambda, as well as the vacuum expectation value upsilon and the coupling constant lambda of the Higgs field. Keeping lambda small, we find there are two critical values of the cosmological constant, Lambda(cr(1)) (upsilon) and Lambda(cr(2)) (upsilon), which depend on upsilon. If Lambda(cr(1)) (upsilon) < Lambda(< 0), we find the first order transition, whereas if Lambda(cr(2)) (upsilon) < Lambda < Lambda(cr(1)) (upsilon), the transition becomes second order. For the case of Lambda(b) (upsilon) < Lambda < Lambda((2)) (upsilon), we again find the first order irreversible transition from the monopole black hole to the extreme Reissner-Nordstrm black hole. Beyond Lambda(b) (upsilon), no monopole black hole exists. We also discuss thermodynamical properties of the monopole black hole in a thermal bath system.

© 2016 American Physical Society.The gravitational baryogensis may not generate a sufficient baryon asymmetry in the standard thermal history of the Universe when we take into account the gravitino problem. Hence, it has been suggested that anisotropy of the Universe can enhance the generation of the baryon asymmetry through the increase of the time change of the Ricci scalar curvature. We study the gravitational baryogenesis in the presence of anisotropy, which is produced at the end of an anisotropic inflation. Although we confirm that the generated baryon asymmetry is enhanced compared with the original isotropic cosmological model, taking into account the constraint on the anisotropy by the recent CMB observations, we find that it is still difficult to obtain the observed baryon asymmetry only through the gravitational baryogenesis without suffering from the gravitino problem.

© 2016 American Physical Society.Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in general relativity (GR). On the other hand, for the solution in Class [II], the Vainshtein screening mechanism works well even in a relativistic star and the result in GR is recovered.

We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Hořava-Lifshitz theory, which is composed of the z=2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. Whereas, if a three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns out to be a spacelike singularity.

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaître-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaitre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stuckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

We argue a scenario motivated by the context of string landscape, where our Universe is produced by a new vacuum bubble embedded in an old bubble and these bubble universes have not only different cosmological constants, but also their own different gravitational constants. We study these effects on the primordial curvature perturbations. In order to construct a model of varying gravitational constants, we use the Jordan-Brans-Dicke theory where different expectation values of scalar fields produce difference of constants. In this system, we investigate the nucleation of the bubble universe and the dynamics of the wall separating two spacetimes. In particular, the primordial curvature perturbation on superhorizon scales can be affected by the wall trajectory as the boundary effect. We show how the gravitational constant in the exterior bubble universe modifies the power spectrum, that provides a peak like a bump feature at a large scale.

We study the origin of dark matter based on the ghost-free bigravity theory with twin matter fluids. The present cosmic acceleration can be explained by the existence of graviton mass, while dark matter is required in several cosmological situations (the galactic missing mass, the cosmic structure formation and the cosmic microwave background observation). Assuming that the Compton wavelength of the massive graviton is shorter than a galactic scale, we show the bigravity theory can explain dark matter by twin matter fluid as well as the cosmic acceleration by tuning appropriate coupling constants.

We study gravitational theories with a cosmological constant and the Gauss-Bonnet curvature squared term and analyze the possibility of de Sitter expanding spacetime with a constant internal space. We find that there are two branches of the de Sitter solutions: both the curvature of the internal space and the cosmological constant are (1) positive and (2) negative. From the stability analysis, we show that the de Sitter solution of the case (1) is unstable, while that in the case (2) is stable. Namely de Sitter solution in the present system is stable if the cosmological constant is negative. We extend our analysis to the gravitational theories with higher-order Lovelock curvature terms. Although the existence and the stability of the de Sitter solutions are very complicated and highly depend on the coupling constants, there exist stable de Sitter solutions similar to the case (2). We also find de Sitter solutions with Hubble scale much smaller than the scale of a cosmological constant, which may explain a discrepancy between an inflation energy scale and the Planck scale.

We study dynamics of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime based on the ghost-free bigravity theory. Assuming the coupling parameters guaranteeing the existence of de Sitter space as well as Minkowski spacetime, we find two stable attractors for spacetime with "twin" dust matter fields: One is de Sitter accelerating universe and the other is matter dominated universe. Although a considerable number of initial data leads to de Sitter universe, we also find matter dominated universe or spacetime with a future singularity for some initial data. The cosmic no-hair conjecture does not exactly hold, but the accelerating expansion can be found naturally. The Lambda-CDM model is obtained as an attractor. We also show that the dark matter component in the Friedmann equation, which originates from another twin matter, can be about 5 times larger than the baryonic matter, by choosing the appropriate coupling constants.

We study Bianchi cosmologies in the ghost-free bigravity theory, assuming both metrics to be homogeneous and anisotropic and of the Bianchi class A, which includes types I, II, VI0, VII0, VIII, and IX. We assume the Universe to contain a radiation and a nonrelativistic matter, with the cosmological term mimicked by the graviton mass. We find that, for generic initial values leading to a late-time self-acceleration, the Universe approaches a state with nonvanishing anisotropies. The anisotropy contribution to the total energy density decreases much slower than in General Relativity and shows the same falloff rate as the energy of a nonrelativistic matter. The solutions show a singularity in the past, and in the Bianchi IX case, the singularity is approached via a sequence of Kasner-like steps, which is characteristic of a chaotic behavior.

The stealth scalar field is a nontrivial configuration without any backreaction to geometry, which is characteristic for nonminimally coupled scalar fields. Studying the creation probability of the de Sitter universe with a stealth scalar field by Hartle and Hawking's semiclassical method, we show that the effect of the stealth field can be significant. For the class of scalar fields we consider, creation with a stealth field is possible for a discrete value of the coupling constant, and its creation probability is always less than that with a trivial scalar field. However, those creation rates can be almost the same depending on the parameters of the theory. DOI: 10.1103/PhysRevD.86.124045

We present the time-dependent solutions corresponding to the dynamical D-brane with angles in ten-dimensional type II supergravity theories. Our solutions with angles are different from the known dynamical intersecting brane solutions in supergravity theories. Because of our ansatz for fields, all warp factors in the solutions can depend on time. Applying these solutions, we construct cosmological models from those solutions by smearing some dimensions and compactifying the internal space. We find the Friedmann-Lemaitre-Robertson-Walker cosmological solutions with power-law expansion. We also discuss the dynamics of branes based on these solutions. When the spacetime is contracting in ten dimensions, each brane approaches the others as the time evolves. However, for a Dp-brane (p <= 7) without smearing branes, a singularity appears before branes collide. In contrast, the D6-D8-brane system or the smeared D(p - 2) - Dp-brane system with one uncompactified extra dimension can provide an example of colliding branes (and collision of the universes), if they have the same charges.

We study a vacuum Bianchi IX universe in the context of Horava-Lifshitz gravity. In particular, we focus on the classical dynamics of the universe and analyze how anisotropy changes the history of the universe. For small anisotropy, we find an oscillating universe as well as a bounce universe just as the case of the Friedmann-Lemaitre-Robertson-Walker spacetime. However, if the initial anisotropy is large, we find the universe which ends up with a big crunch after oscillations if a cosmological constant Lambda is zero or negative. For Lambda > 0, we find a variety of histories of the universe, that is a de Sitter expanding universe after oscillations in addition to the oscillating solution and the previous big crunch solution. This fate of the universe shows sensitive dependence of initial conditions, which is one of the typical properties of a chaotic system. If the initial anisotropy is near the upper bound, we find the universe starting from a big bang and ending up with a big crunch for Lambda <= 0, and a de Sitter expanding universe starting from a big bang for Lambda > 0.

The objectives of the DECi-hertz Interferometer Gravitational Wave Observatory (DECIGO) are to open a new window of observation for gravitational wave astronomy and to obtain insight into significant areas of science, such as verifying and characterizing inflation, determining the thermal history of the universe, characterizing dark energy, describing the formation mechanism of supermassive black holes in the center of galaxies, testing alternative theories of gravity, seeking black hole dark matter, understanding the physics of neutron stars and searching for planets around double neutron stars. DECIGO consists of four clusters of spacecraft in heliocentric orbits; each cluster employs three drag-free spacecraft, 1000 km apart from each other, whose relative displacements are measured by three pairs of differential Fabry-Perot Michelson interferometers. Two milestone missions, DECIGO pathfinder and Pre-DECIGO, will be launched to demonstrate required technologies and possibly to detect gravitational waves.

Supersymmetric solutions of supergravity have been of particular importance in the advances of string theory. This article reviews the current status of black hole solutions in higher-dimensional supergravity theories. We discuss primarily the gravitational aspects of supersymmetric black holes and their relatives in various dimensions. Supersymmetric solutions and their systematic derivation are reviewed with prime examples. We also study the stationary or dynamically intersecting branes in ten and eleven-dimensions, which provide a number of interesting black objects via the dimensional reduction and duality transformations.

Starting with an aspect of motivation to study higher dimensional black holes, we give a brief overview of the whole volume. Finally we give a short note on notations and conventions.

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order "Killing spinor" equation in "fake supergravity" coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial "Killing spinor," which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.

An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state (P = w rho with -1 <= for all w <= 1). It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter [the ratio of the energy density of U(1) fields to that of the scalar field]. The horizon is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature.

We construct a general family of supersymmetric solutions in time- and space-dependent wave backgrounds in general supergravity theories describing single and intersecting p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. We discuss how many degrees of freedom we have in the solutions. We also propose that these solutions can be used to describe higher-dimensional time-dependent "black holes", and discuss their property briefly.

We study physical properties and global structures of a time-dependent, spherically symmetric solution obtained via the dimensional reduction of intersecting M-branes. We find that the spacetime describes a maximally charged black hole which asymptotically tends to the Friedmann-Lemaitre-Robertson-Walker universe filled by a stiff matter. The metric solves the field equations of the Einstein-Maxwell-dilaton system, in which four Abelian gauge fields couple to the dilation with different coupling constants. The spacetime satisfies the dominant energy condition and is characterized by two parameters, Q and tau, related to the Maxwell charge and the relative ratio of black-hole horizon radii, respectively. In spite of the nontrivial time dependence of the metric, it turns out that the black-hole event horizon is a Killing horizon. This unexpected symmetry may be ascribed to the fact that the 11-dimensional brane configurations are supersymmetric in the static limit. Finally, combining with laws of the trapping horizon, we discuss the thermodynamic properties of the black hole. It is shown that the horizon possesses a nonvanishing temperature, contrary to the extremal Reissner-Nordstrom solution.

We present the black hole solutions and analyze their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.

We present the black hole solutions and analyze their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well-defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular at the apex, may be used to provide counterexamples to the conjecture. The physical implications of these counterexamples in curved spacetimes are discussed from various points of view, ranging from classical general relativity, brane physics and holographic models of fundamental interactions.

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional super-gravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations.

In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant (or a vacuum energy) behave as attractors independently of the initial values. We develop a general formulation in terms of two-dimensional phase space, mainly according to the Brans-Dicke model requiring the scalar field decoupled from the matter Lagrangian in the Jordan frame. We show that there are two kinds of fixed points, one of which is an attractor depending on the coupling constant and equation of state. We find that the static universe in the Jordan frame is an attractor in the presence of a cosmological constant for some range of the coupling constant. We extend our analysis to a power-law potential, finding a new type of power-law inflation caused by the coupling to the matter fluid, also as an attractor.

We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

Although f(R) modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the f(R) models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale mu less than or similar to 10(-19) GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale, and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable f(R) models without very careful and unnatural fine-tuning.

Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer infrared divergence, we consider the IR regularization to obtain the finite value. We find that the loop corrections to the scalar perturbations are amplified by the e-folding; in other words there appears the logarithmic correction, just as discussed by M. Sloth et al. On the other hand, we find that the tensor perturbations do not suffer from infrared divergence.

Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such f(R) theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of f(R) models.

Analyzing a capillary minimizing problem for a higher-dimensional extended fluid, we find that there exist startling similarities between the black hole-black string system (the Gregory-Laflamme instability) and the liquid drop-liquid bridge system (the Rayleigh-Plateau instability), which were first suggested by a perturbative approach. In the extended fluid system, we confirm the existence of the critical dimension above which the non-uniform bridge (NUB, i.e., Delaunay unduloid) serves as the global minimizer of surface area. We also find a variety of phase structures (one or two cusps in the volume-area phase diagram) near the critical dimension. Applying a catastrophe theory, we predict that in the 9-dimensional (9D) space and below, we have the first order transition from a uniform bridge (UB) to a spherical drop (SD), while in the 10D space and above, we expect the transition such that UB -> NUB -> SD. This gives an important indication for a transition in the black hole-black string system. (C) 2008 Elsevier B.V. All rights reserved.

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon-crossing time is smaller than some critical value (similar to vertical bar slow-roll parameter vertical bar(-1)), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

We study collision of two domain walls in five-dimensional (5D) spacetime and creation of matter fields. This may provide the reheating mechanism in cosmological models based on a colliding-brane scenario such as the ekpyrotic (or cyclic) universe.
We first analyze the dynamics of colliding domain walls both in 5D Minkowski background spacetime and in asymptotic AdS spacetime including self-gravity. We find that multiple bounces appear at collision. In the case with gravity, we find that a spacelike curvature singularity is formed in the bulk, but it is covered by a horizon.
Next we analyze production of particles at collision of two domain walls. For a scalar 0 where g is a field, the energy density of created particles is evaluated as rho approximate to 20(g)(-4) Nb m(Phi)(4) coupling constant of particles to a domain-wall scalar field, Nb is the number of bounces at the collision and m Phi is a fundamental mass scale of the domain wall. We also study the behaviour, of 5D fermions localized on domain walls, when two walls collide in a 5D Minkowski background spacetime. For kappa = 0 mode, we find that most fermions are localized on both branes as a whole even after collision. However, how much fermions are localized on which brane depends sensitively on the incident velocity and the coupling constants.

We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase in which particle motion becomes nearly regular (so-called "stagnant motion" or stickiness) for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviors affect observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different chaotic behaviors of the orbit via the gravitational waves.

We study the dynamics of colliding domain walls including self-gravity. The initial data is set up by applying a Bogomol'nyi-Prasad-Sommerfield (BPS) domain wall in five-dimensional supergravity, and we evolve the system determining the final outcome of collisions. After a collision, a spacelike curvature singularity covered by a horizon is formed in the bulk, resulting in a black brane with trapped domain walls. This is a generic consequence of collisions, except for nonrelativistic weak field cases, in which the walls pass through one another or multiple bounces take place without singularity formation. These results show that incorporating the self-gravity drastically changes a naive picture of colliding branes.

We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we show that these solutions include the BMPV black hole and the Brinkmann wave solution. We also find new solutions similar to the Brinkmann wave. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field ℱij, which is a rotational part of gravity, is self-dual. We also discuss non-spherical "black" objects (e.g., a ring topology and an elliptical shape) by use of other curvilinear coordinates. © 2006 IOP Publishing Ltd.

We study the evolution of a five-dimensional rotating black hole emitting scalar field radiation via the Hawking process for arbitrary initial values of the two rotation parameters a and b. It is found that any such black hole whose initial rotation parameters are both nonzero evolves toward an asymptotic state a/M-l/2 = b/M-1/2 = const(not equal 0), where this constant is independent of the initial values of a and b.

We study inflationary solutions in the M-theory. Including the fourth-order curvature correction terms, we find three generalized de Sitter solutions, in which our 3-space expands exponentially. Taking one of the solutions, we propose an inflationary scenario of the early universe. This provides us a natural explanation for large extra dimensions in a brane world, and suggests some connection between the 60 e-folding expansion of inflation and TeV gravity based on the large extra dimensions. (C) 2004 Elsevier B.V. All rights reserved.

It has been known that a B=2 skyrmion is axially symmetric. We consider the Skyrme model coupled to gravity and obtain static axially symmetric regular and black hole solutions numerically. Computing the energy density of the skyrmion, we discuss the effect of gravity to the energy density and baryon density of the skyrmion.

We investigate spherically symmetric self-similar solutions in Brans-Dicke theory. Assuming a perfect fluid with the equation of state p=(gamma-1)mu(1less than or equal togamma<2), we show that there are no nontrivial solutions which approach asymptotically to the flat Friedmann-Robertson-Walker spacetime if the energy density is positive. This result suggests that primordial black holes in Brans-Dicke theory cannot grow at the same rate as the size of the cosmological particle horizon.

We study a new quintessence scenario by a scalar field with an inverse-power potential based on the brane cosmology. We show that in the quadratic dominant stage, which generically appears in brane world cosmology, the density parameter of a scalar field Omega(phi) decreases regardless of the potential-term contribution. This feature enables us to impose natural initial condition. We also discuss the constraints on parameters for the natural and successful quintessence scenario. (1)).

We present the analytic solution of N Einstein-Rosen bridges (''N black holes'') in the space-time with a cosmological constant LAMBDA and analyze it for one- and two-bridge systems. We discuss the three kinds of apparent horizons: i.e., the black-hole, white-hole, and cosmological apparent horizons. In the case of two Einstein-Rosen bridges, when the ''total mass'' is larger than a critical value, the black-hole apparent horizon surrounding two Einstein-Rosen bridges is not formed even if the distance is very short. Furthermore, in this case, the cosmological apparent horizon enclosing both bridges does not appear. Hence, it seems that when the ''total mass'' is very large, the Einstein-Rosen bridges cannot collapse into one black hole unless the ''gravitational mass'' is released in some way.

In this project, we have conducted theoretical investigations on the evolution of massive stars from the quasi-static phase through the gravitational core-collapse and the subsequent supernova explosion up to the formation of a neutron star or a black hole. We have first performed approximate simulations of core-collapse and explosion for several hundreds of models and made clear that the compactness of the stellar core just prior to the collapse is the single most important quantity to determine the success or failure of explosion. We have also accomplished more rigorous simulations on the K supercomputer and demonstrated that the most sophisticated computations cannot reproduce the supernova explosion. We have then upgraded our code so that general relativity could be handled. We have finally developed a novel formulation to numerically obtain various stellar configurations in rotational equilibrium so that we could study the effect of rotation on the evolution of massive stars

宇宙論の標準モデルであるﾋﾞｯｸﾞﾊﾞﾝ宇宙論は、近年の精密観測により確かなものになってきたが、その一方で新たな謎としてﾀﾞｰｸｴﾈﾙｷﾞｰ問題が誕生した。その解決には自然界における基本法則の根幹にも関わる発想の転換が必要と考えられる。また、ミクロ世界においてはｲﾝﾌﾚｰｼｮﾝ宇宙論などの初期宇宙像の観測的検証が注目されており、素粒子統一理論をもとにしたその基本的理解が求められている。これらミクロとマクロの両極端で謎となっている加速膨張宇宙の起源の解明には宇宙を支配する重力の本質的理解が鍵となり、一般相対性理論を超えた様々な重力理論が提案されるに至っている。本研究では、超弦理論など素粒子統一理論の立場からﾀﾞｰｸｴﾈﾙｷﾞｰ・ｲﾝﾌﾚｰｼｮﾝなどの宇宙の未解決重要課題を重力物理学の問題として系統的に解析する。
2013年度は主に以下の研究成果を得ている。
(I)素粒子統一理論を基礎にした様々な重力理論に基づくｲﾝﾌﾚｰｼｮﾝの解析を行っているが、近年ｹﾞｰｼﾞ場とｲﾝﾌﾗﾄﾝ場の結合の重要性が指摘されており、2013年度は、特に、ｹﾞｰｼﾞ場のｲﾝﾌﾚｰｼｮﾝﾓﾃﾞﾙに与える影響を解析した。複数のU(1) ｹﾞｰｼﾞ場またはSU(2) ｹﾞｰｼﾞ場がｲﾝﾌﾗﾄﾝ場と結合する場合、一様等方加速膨張時空が安定解として存在するが、初期の非等方性が大きい場合は、長期間非等方加速膨張が起こり、モデルが観測的に検証可能であることを示した。
(II)ﾀﾞｰｸｴﾈﾙｷﾞｰ問題に関しては、2013年度は、massive gravity 理論を拡張したbigravity理論を基礎に解析した。その結果、加速膨張宇宙がｱﾄﾗｸﾀｰとして動的に実現されるということ、さらには第二の計量と結合する「双子物質」が我々の宇宙のﾀﾞｰｸﾏﾀｰとして振る舞う可能性があることを示した。

We analyse various gravity theories which may resolve two most important subjects in modern cosmology (inflation and dark energy problem) based on the unified theory of fundamental interactions. We propose two new inflationary scenarios (Higgs inflation based on standard model of particle physics and KKLMMT inflation based on superstring theory), which are extended from the original models and satisfy the observational constraints well. As for the dark energy problem, we mainly analyse bigravity theory, in which one of gravitons is massive. We show that it may resolves the dark matter problem as well as the dark energy problem

We study most fundamental and important subjects on cosmology as gravitational physics. As for the subject on the early universe, we analyze the so called cosmological singularity problem by Horava-Lifshitz gravity theory and the origin of inflation based on superstring theory. We also study dark energy problem mainly by a bigravity theory. We find that dark energy (a cosmological constant) naturally appears as an attractor in this model

研究結果：日英の重力理論および宇宙論研究の第一線で活躍する研究者が、素粒子統一理論から予言される高次元宇宙における宇宙論を基礎に宇宙論の諸問題解明に取り組んだ。

2000年に始まったブレイン宇宙論の研究を、この分野の第一線で活躍している日英の研究者を集め集中的に行った。期間中に行ったワークショップにおいては、次代の宇宙論としての可能性を探った。

In Nasu Observatory, Radio Transient Sources were discovered with spherical dish array at 1.4GHz. These discoveries were investigated in the following Journals. In X and Gamma-ray astronomy as well as in optical astronomy, we have facilities having large field of view to detect transient objects. One example was Gamma-ray Bursts. It took more than 30 years to understand they were cosmological objects. In radio waves, transient sources in Galactic plane were known in early seventies. Typical one was Cyg-X3, in which large outbursts were observed once a year or so. However, no radio transients was known at high Galactic latitudes until Nasu Observatory started observation in 2000. We have developed Large Spherical Dish Array Interferometer at very low cost. We also developed digital signal processing system to search large field of view. As a result, we found several radio transients at high Galactic latitudes.

In this research, we investigated the problems on the generality of inflation, by which we can believe the present homogeneity and isotropy of the Universe, and found the following results.
1. The main theme in this research is whether the universes which were created anisotropically or inhomogeneously call evolve into the present universe through inflation. As for this problem, we clarified the followings: (1) For the homogeneous but anisotropic universe, we know that any spacetimes except for Bianchi type IX always approach the inflationary solution. For Bianchi type IX spacetime, however, the results depend on the initial conditions of the universe, hence we showed from the quantum cosmological point of view that initial conditions which drive the universe into inflation are quite natural. (2) As for inhomogeneous spacetimes, we adopted two methods: (i) Two analytic approaches for symmetric spacetime: one is the so-called "inverse scattering method", and the other the Israel's thin shell method. In both case, we obtained inhomogeneous solutions with a cylindrical or plane- symmetry in de Sitter background, discussing about the cosmic no-hair conjecture. (ii) Numerical Approach for most general three-dimensional spacetime We first calculated a spherically symmetric case, and then started to study the most general three-dimensional case. We developed a new formalism, which will be convenient to simulate the cosmological model in the context of numerical relativity. We discussed how to choose a time slicing in the universe and also found a general solution for the linearized gravitational waves in de Sitter background, discussing the homogenization mechanism of inhomogeneities of spacetimes.
2. The unified theories of the fundamental interactions may predict a modification of the Einstein theory at the high energy scale. A quantum corrections provide higher-derivative terms of the metric tensor and a non-minimal couping to scalar fields. Brans-Dicke type theories may be derived from higher-dimensional theories such as a superstring. We investigated whether inflation is a natural phenomenon even in such a generalized Einstein theory. Applying a conformal transformation of the metric tensor, we find that most theories are equivalent to the Einstein theory. Using this equivalence, we found that inflation is a natural phenomenon in most cases.

In this research, we discussed the problems on inhomogeneity of the Universe, in particular, on creation and evolution of inhomogeneous spacetime.1. The one of main topics in this research is whether the inhomogeneous universes evolve into the present universe through inflation. In order to investigate this subject, we first presented a formalism of numerical cosmology, which is a natural extension of numerical relativity for gravitational collapse.(1) We found the following two results :(i) Goldwirth and Piran calculated 1 dimensional spherically symmetric case, while we discussed 1 dimensional planar symmetric spacetime with cosmological constant in order to discuss inhomogeneity due to gravitational waves. We found that all spacetime evolve into de Sitter space. This strongly supports the cosmic no-hair conjecture.(ii) From our simulation and by an analysis of exact solutions, we proposed "Cosmic Hoop Conjecture" by which we can discuss on an inflationary scenario for general inhomogeneous spacetime.(2) For the homogeneous but anisotropic universe, we generalized Wald's theorem for the case of power-law inflation, which may be realized in generalized einstein theories discussed below.2. We also considered cosmology in generalized Einstein theories (GETs) such as Brans-Dicke theory. :(1) Although new and chaotic inflation need a fine-tuning in coupling constants, if we consider those in GETs, then such constraints is loosened. We call this model soft inflation.(2) In extended inflation, nucleated bubbles produce inhomogeneity of the Universe. The original model seems to be excluded from observation by a rough analysis of bubble expansion. However, we found by a detailed analysis that bubbles are nucleated in the Hawking-Moss mode instead of the Coleman-De Lucia mode, and the thin wall approximation is broken in an initial stage of inflation. This may change a scenario of the extended inflation model.(3) The structure formation in the Universe is one of the most important topics in cosmology, but no one knows yet what is a real mechanism. Using GETs, we looked for a new mechanism. In particular, we considered the theory with non-minimal coupling, which predicts an oscillation in Hubble parameter and then provides us a slow expanding phase of the Universe. We, hence, expect a rapid growth of the density perturbations in the slow expansion phase. For some parameters, we really found a large enhancement of the density perturbations. Unfortunately, the Universe must had an unphysical era in the past, when the effective gravitational constant was negative

重力波を含めた一般相対論における非線型動的現象の研究は、方程式の非線型性のため解析的アプローチにおいては、従来、問題個々に限られた範囲でのみ考察されていた。そのいくつかは非常に興味深にもので、非線型物理学としての一般相対論は一部確立されている(逆散乱法を用いた解の生成法、膨張宇宙でのソリトン解、宇宙初期やブラックホールのまわりの粒子のカオス的振舞いなど)。しかし解析的にアプローチするには限界があり、その限界を数値的相対論を使って越えようとしたり解析的アプローチと数値的相対論との融合により、一般相対論の基礎的研究を行うという試みはいまだかってあまり行われておらず、それを重力波の動的振舞いに焦点をしぼり系統的に行うというのが本研究の特徴である。現在までに、おもに京都グループと共同で、膨張宇宙における重力波の非線型振舞いについて研究を行っている。重力波は、それ自身ブラックホールを形成するほどにその非線型性が大きくなりうるが、逆に宇宙膨張はその形成を妨げようとする。その競合過程を研究することで、重力波の非線型的性質、振舞い等についてより深い理解が出来ると考えられる。またこの研究は、宇宙論におけるインフレーションの必然性の議論においても重要になり、我々のこれまでの研究で、非一様な初期宇宙の進化についてかなり多くのことが明らかになった。さらに、我々は、現在世界的に活躍している日本人相対論研究者と相互に連絡をとり、本研究課題を拡張したテーマで「一般相対論と重力」研究会をスタートしている。本年度は、93年1月に早稲田大学で開催した。参加者は予想を上回り140名以上で、多くの若手研究者の参加、研究発表(60講演)があり、この分野の研究会としては盛況なものになった。これらの成果は英文の報告集としてまとめられている。この研究会をきっかけとして、さらに多くの研究者がこの重点領域研究に興味を持ち、重点領域推進の一助となることが期待され、そのためにも、今後も年一回の研究会を開催する予定である

We investigate dynamics of inhomogeneous spacetime with a cosmological constant and find a universal picture : There is a critical value of the Abbott-Deser mass, beyond which localized inhomogeneities do not collapse into black holes. Consequently, black holes with large mass cannot be formed in the asymptotically de Sitter space-time, unless a naked singularity is formed. This result suggests a possible inflationary scenario for inhomogeneous universes

重力波を含めた一般相対論における非線型動的現象の研究は、方程式の非線型性のため解析的アプローチにおいては、従来、問題個々に限られた範囲でのみ考察されていた。そのいくつかは非常に興味深にもので、非線型物理学としての一般相対論は一部確立されている(逆散乱法を用いた解の生成法、膨張宇宙でのソリトン解、宇宙初期やブラックホールのまわりの粒子のカオス的振舞いなど)。しかし解析的にアプローチするには限界があり、その限界を数値的相対論を使って越えようとしたり解析的アプローチと数値的相対論との融合により、一般相対論の基礎的研究を行うという試みはいまだかってあまり行われておらず、それを重力波の動的振舞いに焦点をしぼり系統的に行うというのが本研究の特徴である。現在までに、おもに京都グループと共同で、膨張宇宙における重力波の非線型振舞いについて研究を行っている。重力波は、それ自身ブラックホールを形成するほどにその非線型性が大きくなりうるが、逆に宇宙膨張はその形成を妨げようとする。その競合過程を研究することで、重力波の非線型的性質、振舞い等についてより深い理解が出来ると考えられる。またこの研究は、宇宙論におけるインフレーションの必然性の議論においても重要になり、我々のこれまでの研究で、非一様な初期宇宙の進化についてかなり多くのことが明らかになった。さらに、我々は、現在世界的に活躍している日本人相対論研究者と相互に連絡をとり、本研究課題を拡張したテーマで「一般相対論と重力」研究会をスタートしている。本年度は、93年1月に早稲田大学で開催した。参加者は予想を上回り140名以上で、多くの若手研究者の参加、研究発表(60講演)があり、この分野の研究会としては盛況なものになった。これらの成果は英文の報告集としてまとめられている。この研究会をきっかけとして、さらに多くの研究者がこの重点領域研究に興味を持ち、重点領域推進の一助となることが期待され、そのためにも、今後も年一回の研究会を開催する予定である

Because of recent important observations and experiments of gravity or progress of computer science, we are now in the most exciting epoch of general relativity and gravitation after Einstein's theory of general relativity. Taking this opportunity, we had planned a systematic collaboration for several important subjects on relativity and gravity by prominent researchers. The subjects we studied are classified into three categories :(1) Fundamental problems in general relativity and gravitational wave astronomy (analytic approach : T.Futamase, K.Maeda, T.Nakamura, M.Sasaki, A.Tomimatsu ; numerical approach : Y.Eriguchi, H.Ishihara, Y.Kojima, T.Nakamura, K.Oohara, H.Shinkai)(2) Fundamental problems in relativistic cosmology (T.Futamase, A.Hosoya, Y.Kojima, K.Maeda)(3) Fundamental problems in particle physics and gravity (H.Ishihara, H.Kodama, K.Maeda, M.Sasaki, A.Tomimatsu, M.Yoshimura)In addition, we held three conferences on general relativity and gravitation each year for all researchers in this field to get together and to have discussions. For each conference, the number of participants was about 150 and we had beyond 50 talks. The results are published in the proceedings in Englishi. We also had several workshops by small numbers of researchers and students to make intensive discussion and collaborations

重力波を含めた一般相対論における非線型動的現象の研究は、方程式の非線型性のため解析的アプローチにおいては、従来、問題個々に限られた範囲でのみ考察されていた。そのいくつかは非常に興味深にもので、非線型物理学としての一般相対論は一部確立されている(逆散乱法を用いた解の生成法、膨張宇宙でのソリトン解、宇宙初期やブラックホールのまわりの粒子のカオス的振舞いなど)。しかし解析的にアプローチするには限界があり、その限界を数値的相対論を使って越えようとしたり解析的アプローチと数値的相対論との融合により、一般相対論の基礎的研究を行うという試みはいまだかってあまり行われておらず、それを重力波の動的振舞いに焦点をしぼり系統的に行うというのが本研究の特徴である。現在までに、おもに京都グループと共同で、膨張宇宙における重力波の非線型振舞いについて研究を行っている。重力波は、それ自身ブラックホールを形成するほどにその非線型性が大きくなりうるが、逆に宇宙膨張はその形成を妨げようとする。その競合過程を研究することで、重力波の非線型的性質、振舞い等についてより深い理解が出来ると考えられる。またこの研究は、宇宙論におけるインフレーションの必然性の議論においても重要になり、我々のこれまでの研究で、非一様な初期宇宙の進化についてかなり多くのことが明らかになった。さらに、我々は、現在世界的に活躍している日本人相対論研究者と相互に連絡をとり、本研究課題を拡張したテーマで「一般相対論と重力」研究会をスタートしている。本年度は、93年1月に早稲田大学で開催した。参加者は予想を上回り140名以上で、多くの若手研究者の参加、研究発表(60講演)があり、この分野の研究会としては盛況なものになった。これらの成果は英文の報告集としてまとめられている。この研究会をきっかけとして、さらに多くの研究者がこの重点領域研究に興味を持ち、重点領域推進の一助となることが期待され、そのためにも、今後も年一回の研究会を開催する予定である

We have analyzed a property and stability of new type of black holes, which do not belong to the Kerr-Newman family. In a unified theory of fundamental interactions, we usually expect non-Abelian gauge fields, which provide us new types of non-trivial structure like a monopole and new black holes. We have classified those black holes and presented a unified picture. We have also shown that the stability of those black holes is understood by a catastrophe theory, when the entropy of a black hole is regarded as the potential function.The qunatum radiation process of black holes has also been studied in theories with a dilaton field, which is inspired by a unified theory. A superstring model turns out to be critical in a sense that the energy flux of Hawking radiation diverges if the dilaton coupling with U (1) gauge field is larger than that of the superstring model

1) Neutrino Background Radiation due to Supernove ExplosionRecently Superkamiokande project has started and it can observe the relic neutrino through supernove explostion. We investigated carefuly the spectrum of relic neutrino using the model for the chemical evolution of galaxies. The total flux depends strongly on the Hubble parameter, but weakly on the cosmological constant. We found that in the same flat universe model the flux in lambda=0 is smaller than that in lambda*o.2) Primordial NucleosynthesisThe primordial nucleosynthesis is best tool for deciding the baryon density. Recently, associated with the progress of techonology in obsevational field, the obsevational result pointed out that the simple model for cosmology has a trouble point. Some of people call the problem as 'crisis' in the universe. Hence, we taken account of the theoretical error in the lepton asymmetry universe and estimeted statistically the final fraction of the light elements by Monte Calro simulation. The result is that the best values for the degenerate parameter and the baryon density are 0.043(]SY.+-。[)0.040 and 0.015(]SY.+-。[)0.006-0.003 (CL.95 percent)

(ナイキストレートでの空間時間FFT)世界ではじめて、ナイキストレートで処理を行う空間時間FFTプロセッサーを開発し(Daishido,T.et al,2000)、64台のアンテナからなる干渉計に接続して、64方向、256チャネル同時観測を実現した。(信号の流れのトポロジー)このプロセッサーの開発・製作過程では多くの工夫がなされ、世界に新しい流れをつくりだした。第一は、空間処理FFTと時間処理FFTの信号の流れのトポロジーが全く同じであることを積極的に利用して、全く同じ構造のプロセッサー2組で空間時間FFTを一挙に実現したことである。(空間時間データの並べ換え)間に設置した空間時間データ変換部の設計には、大いに頭をしぼったが、完全に作動し、見通しの正しかったことが確認できた。実際、空間FFTの基板と時間FFTの基板を交換しても動くことを確かめてある。このことにより、メインテナンスが楽になり、製作経費が低く押さえられた。トポロジーは同じであるが、FFTのバタフライ演算に設定する位相回転子はもちろん異なる。(Radix-4 FFT バタフライLSIの設計)設計の主要部分は研究室が関わり、Radix-4演算を行うLSIの設計は、博士課程在学中の田中(Tanaka,N.et al,2000)が中心に行った。空間16×16、時間256、のFFTのトポロジーが同一なので、ハードウエアとしては同一のプリント基板を使い、空間FFT(16枚、2ブロック)、時間FFT(16枚2ブロック)で構成し、中間のST変換部でデータの並べ換えを行う。基板の総数は、64枚となる。各基板は、16複素入力、同出力、となるので、バタフライLSIは、初段に4個、2段目に4個の計8個が実装される。LSIの総数は、8×64=512個となり、カスタムLSI(ASIC)で製作した。数が多いのでFPGAで構成するときの1/10のコストで実現できた

In this study project we covered the general-relativistic astrophysical phenomena on all space-and-time scales of the Universe and tried to clarify their mutual connections. The studies were performed for 4 years from 2000 to 2003 fiscal year, and many valuable results were obtained. They are classified into three groups : (1) the space-time structure at the very early stages in the neighborhood of the big-bang, (2) phenomena on spatially small scales (gravitational waves, high density stars and black holes), and (3) phenomena on spatially large scales (the non-uniformity, large-scale structures and gravitational lensing). In each of them, the remarkable results are that (1) theories on the multidimensional brane world and our Universe as its four-dimensional section were introduced and studied extensively, (2) the framework of gravitational-wave astrophysics was constructed and the formation mechanism of gamma-ray bursts began to be clarified, and (3) various cosmological observations (like WMAP, SDSS etc) were executed, the cosmological model parameters were determined assuming the cosmological principle and the existence of dark energy was clarified. Many of these results were reported in the Workshops of General Relativity and Gravitation held in Osaka University, Waseda University, University of Tokyo and Osaka City University, and in Workshop of "Frontiers of Cosmology and Gravitation" as well as the other international conferences. These Workshops and conferences were useful for the international communications and the education of young physists in our field

重力波は,重力場の時間変化,つまり物体の運動によって引き起こされるが,強い重力場を伴う現象でないと重力波観測のための源として期待できない.そこでまず重要となる課題は,相対論的力学系における物体運動の解析である.その解析で最も簡単な方法がテスト粒子近似であるが,そのような場合でも系の非可積分性からカオスなどの力学系特有の非線型現象が現れる.実際,回転するカーブラックホールの周りを運動するスピンをもった粒子の運動はある状況でカオス的に振る舞うことが申請者たちによって示されている.その研究を元に,J.Levin博士は一般の連星系においても同じようなカオス的振る舞いが見られ,それが重力波観測に影響することを指摘している.一方,Schnittman博士とRatio博士らの解析ではリャプノフ指数が小さく,合体するときにはカオスが起こる十分な時間がないことを示している.しかし,赤道面を離れた場合のような3次元的な物体運動においてはその多くが明らかにされていない.そこで本研究では,相対論的な力学系(質点+ディスク系およびカー時空のまわりのスピン粒子)を系統的に解析し,系の非線形現象の解明と,それに伴う重力波の研究を行った.特に,粒子がカオス的振る舞いをする場合とそうでない場合の放出重力波の性質(波形.スペクトルなど)のどの部分に違いが現れるかを解析し,観測される重力波から系の運動状態が予測可能かどうか考察した。その結果,カオス的振る舞いをしない系ではエネルギースペクトルにおいて特徴的な波数が存在するのに対し,カオス力学系からの重力波のエネルギースペクトルにはすべての波数の波が出現することがわかった.また,これらの解析を元に相対論的力学系一般における重力波の性質及び役割を明らかにすることができる

The idea of "brane", which appeared in string theory, changes completely the view of the early universe and strong gravitational phenomena. It also changes the view of higher dimensions from the conventional old idea by Kaluza and Klein, i.e., the existence of a brane makes a large extra dimension possible and visible. Furthermore new brane models proposed by Randall and Sundrum give new types of compactification mechanism. Especially, the second model has become the focus of cosmologist's attention because it gives the Newtonian gravity in higher dimensional world without compactification. This model provides definitely a different aspect from the conventional Kaluza-Klein compactification. Hence many relativists and cosmologists are studying it to look for new world view. Under such a circumstance, it is very important to analyze cosmological models and strong gravitational phenomena such as a black hole or gravitational collapse based on this brane gravitational theory. In this research project, we study new view of the brane world with the help of two prominent young professors (David Wands and David Langlois).In order to clarify the properties of brane gravity, we have studied brane collision in the ekpyrotic cosmological model, which could be an alternative of the standard inflation scenario, and the reheating mechanism, which leads the universe to a big bang. We have also analyzed some effective theories with higher curvature terms, which come from quantum correction of string theory discussed their cosmological models, and proposed new inflationary scenario

New idea of gravitation is given from a "brane" in string theory, and it has recently been intensively studied because it may lead to new paradigm of cosmology. In the present research project, we have analyzed systematically fundamental problems in cosmology from the view point of a brane world in order to study new subjects such as what is the fundamental and important in brane gravity or what will be new paradigm of brane cosmology. Especially, studying new gravitational theory with a brane, we have discussed most important subjects in cosmology such as "dark energy", "cosmological constant problem", "creation of the universe" and "cosmological singularity". We have analyzed mainly the following three subjects:(1) The study of the unconventional early universe models based on brane collisionTaking into account self-gravity, we have analyzed a brane collision and shown that a spacetime singularity is formed because of gravitational instability. We have also studied the possibility of creation of matter (the origin of matter) in the universe via a brane collision.(2) The study of the inflation models based on string theoryWe have proposed new inflationary model based on string theory. We have studied the higher curvature terms which appear via quatum corrections in superstring theory. Although we find sufficient expansion of the universe, we need a fine tuning of initial conditions. It suggests that we have to find the proper correction terms with the Ricci curvature tensor as well as the Riemann one.(3) The construction of black hole solutions based on string theoryWe have presented new method to find black hole solutions in string theory. It is generalization of the conventional method using the BPS equations. We have obtained a new black hole (a caged black hole) solution

We study the so called "dark energy problem", which is one of the most important subjects of modern cosmology, from three approaches : (1) exotic fluid of dark energy (2) modified gravity theories (3) the possibility of other natural models. We have pointed out that it is important to analyze a strong gravitational system such as a black hole or a neutron star which is coupled to dark energy

本研究では、AdS/CFT対応を研究する際に重要となる重力サイドの漸近的AdS時空のダイナミクスに特化して研究を遂行した。従来の時空のダイナミクスとは異なる新しい展開が期待できるものとして「AdS時空上におけるカオスなどの非線形現象」があるが、本研究では、Schwarzschild AdS 時空に於ける弦の運動について解析を行い、 winding数が異なる場合には非可積分になり、特に質量が臨界値を越えると強いカオス性を示すことを明らかにした。これらの成果は学術論文として準備中である

本特定課題研究では、現代宇宙論最大の謎であるﾀﾞｰｸｴﾈﾙｷﾞｰ問題に関して、重力子に質量を持たせるmassive gravity 理論を拡張したbigravity理論を基礎に解析した。その中でも特に、第二の計量と結合する「双子物質」に着目し、我々の宇宙のﾀﾞｰｸﾏﾀｰとして振る舞う可能性を精査し、ﾀﾞｰｸﾏﾀｰの3つの必要条件（銀河の回転曲線、構造形成問題、宇宙の構成要素）すべてを満たすことが出来ることを示した。タイトルにあるbigravity理論における重力波に関しては，現在研究が進行中である。

1990年代半ばから始まった大型重力波望遠鏡建設計画は、米国のLIGO、欧州のVIRGOの観測開始，そして日本のKAGRA計画の実質的スタートにより本格的観測が可能な段階に突入し、重力波天文学は現実的なものになってきている。この重力波天文学の重要な目的としては，重力理論の検証，超高密度領域における新しい現象の探求，そして第３の目としての天文学である。一方、ビッグバン標準宇宙論の大成功にもかかわらず、宇宙論では「ダークエネルギー」という大きな謎が出現し、人類は新たな挑戦状を突きつけられている。宇宙の4分の3が宇宙膨張を加速させる未知のエネルギーで占められているという。その正体はまだ全くわかっていないが、一つの可能性として、宇宙規模のスケールでは一般相対性理論が変更を受け、それに代わる新しい重力理論により加速膨張を説明しようというアプローチが提案されている。このような状況においては、重力波天文学の目標の一つである「重力理論の検証」を相対論研究の立場からより真剣に考える必要がある。本研究では、申請者のこれまでの種々の重力理論研究の経験を生かし、そのような新しい重力理論に基づく重力波の研究を行う。その具体的方法および成果は以下の通りである。ダークエネルギーを説明する新しい重力理論としては、量子補正などから期待される曲率高次の項を現象論的に取り入れたf(R)重力理論、基礎方程式が２階微分方程式で表されるガリレオン重力理論、また一般相対性理論の代替理論として従来から研究されているBrans-Dicke 理論やスカラー・テンソル理論、ベクトル場を加えたアインシュタイン・エーテル理論やTeVeS理論、さらには、有限質量の重力子を考える有質量重力理論(massive gravity)や双重力理論(bi-gravity)など、非常に多くの重力理論が提唱されている。本研究では、重力波を用いてそれらの理論を判別する方法としてブラックホールのQuasi Normal Mode（QNM）解析を考える。一般相対性理論において従来から研究されている連星系の合体やそれに伴うブラックホール形成から放出される重力波は重力波天文学の重要なターゲットの一つであるが、その最終段階で放出されるQNM重力波はブラックホールの性質に大きく依存する。ところが重力理論が異なるとブラックホール解やその摂動方程式が異なり、QNM重力波観測が重力理論検証に決定的な役割を果たすと考えられる。そこで、様々な重力理論に基づくブラックホール解の探索とそのQNM解析を目指した。まずその準備段階として、ブラックホール解は必ずしも解析的に得られるとは限らないので、数値解でブラックホールが得られた場合のQNMを求める手法を開発した。また、近年特に注目されている双重力理論においては、質量ゼロの重力子とともに有限質量の重力子が現れ、それが観測的に大きな制限を与えることが予想される。この場合のブラックホールはSchwarzschildまたはSchwarzschild-de Sitter時空で記述されるが、その場合のQNMがどのように得られ、観測的にどのような制限が加わるかという問題に関しては、まだ最終的な結果が得られていなく、近い将来にその研究成果を発表する予定である。

本研究では，非線形物理学の観点から，重力多体系の動的性質について考察した．具体的には、次の二種類のモデルを詳しく解析した．１．まず背景時空は平坦な宇宙であるとして，その中で多くの一次元シートがニュートン重力によって相互作用を及ぼすモデルを解析し，宇宙で観測されるフラクタル構造の起源をさぐった．このシートモデルは解が解析的に記述できるため，長時間の発展を追う事ができる．膨張入りのシートモデルで初期密度ゆらぎをフラクタル的にした場合には，十分に時間が経過した後に非線形なフラクタル構造が形成されるが，そのフラクタル次元は，初期ゆらぎのフラクタル次元によらずほぼ普遍的な次元0.9に収束することがわかった．この普遍性は重力の長距離相互作用を反映したものと考えられる．また，このフラクタル構造は相空間にも特徴を持つ．自己重力により形成された構造はその相空間では渦巻き状の構造をすることが簡単な解析からわかるが，初期にフラクタル的揺らぎをしていると，構造形成後にはその渦巻き構造が入れ子構造をしていることがわかった．この成果を用いると，実際の観測データの解析により密度揺らぎの起源を特定化できる可能性を与える点で注目に値する．２．もう一つのモデルとして，三次元重力の特徴を備えた簡単なモデルを考案した．三次元重力と同じ形の相互作用を及ぼしあう多くの粒子を一次元リングに拘束したモデル（リングモデル）で，このモデルでは特定のエネルギー範囲では比熱が負になり，粒子が密集したコア層の周囲に特異な振る舞いを示すハロー粒子が取り巻くという，三次元重力の特徴が現れる．重力の特徴を解析する上で，このリングモデルは少ない計算量で高い解像度を得る事ができ，フラクタル構造が形成されるかどうかを調べる場合にも有用と考えられる．このモデルを詳細に解析した結果，非ガウス的な速度分布や粒子分布のスケーリング則の起源がガス層とコア層を行き来するハロー粒子の存在にあることを明らかにした．以上の研究により，重力などの長距離相互作用が働く多体系における統計的性質の重要な一面（つまり，フラクタル構造やその次元及び非ガウス的分布など重力多体系において特有に現れる普遍的性質）が明らかにされた．

　ビッグバン宇宙論によると宇宙の始まりは特異点ということになり、そこでは一般相対論は何らかの変更が余儀なくされる。インフレーション宇宙論は、宇宙初期の標準モデルになりつつあるが、特異点問題は解決されない。量子宇宙論がその可能性として考えられるが、もう一つの鍵として素粒子の統一理論がある。統一理論としては、超ひも理論がもっとも有望ではあるが、その宇宙論的応用はまだ十分なものとはいえない。一方、ブラックホールにおいても、ホーキングが1973年にブラックホールの量子論的蒸発を示したが、その最終状態に関してはまだよくわかっていない。そこで、我々は、超ひも理論を基礎にした宇宙初期やブラックホールにおける特異点の振舞いに関し系統的な研究を行った。　超ひも理論では、高エネルギー極限で、通常のアインシュタイン理論とは異なる新しい量子的な効果として曲率高次の項が現れることが予想されている。そこで、我々はまず曲率２次の項として期待されるGauss-Bonnet 項が付加された場合の影響についてブラックホール及び初期宇宙論について特に特異点出現の観点から考察した。また、統一理論で現れるYang-Mills 場（非可換ゲージ場）を伴うブラックホールについても詳細に解析した。さらに宇宙項やディラトン（系に普遍的に現れるスカラー場）の影響についても考察を行った。その結果、これらの効果は必ずしも特異点回避には十分ではなく、特異点のタイプを変更するにとどまることを明らかにした。場の理論的取り扱いを超えたひも理論的な取り扱いの必要性を示唆している。

　Hulse とTaylor の発見した連星パルサーによってその存在が明らかにされた重力波を直接観測しようと、LIGOを初めとする重力波干渉計の大型プロジェクトも着々と進み、２１世紀初めには最初の重力波観測も夢ではなくなった。重力波は従来の電磁波や新しい観測手段のニュートリノでは観測できない星の最終段階や宇宙初期などを見る第３の目として期待されている。もし、その重力波を使った天文学が現実のものとなれば、天文学的重要性に加えて、物理学の基本的な問題にまで迫りうる重力波天文学が可能になる。特に、連星パルサーの合体は重力波源としても有望で、そのテンプレート制作は重力波天文学の理論的最重要課題で、世界各地で研究が続いている。　ところで、天体を記述する天体力学に関しては、ニュートン重力理論を基礎にした研究が非常に活発で、先駆的なポアンカレによる三体問題の研究はもちろん、最近ではコンピュータを使ったより定量的な解析が進み、そのような力学系を非線形物理学の一つの分野として議論するようになってきている。一方、連星パルサーの合体などで重要となるアインシュタインの重力理論は、複雑な非線形偏微分方程式で重力場自身も非線形となるので、ニュートン理論では現れない新しいタイプの非線形現象も期待できるが、その研究はこれまでほとんどなされていない。そのような非線形現象、特にカオスなどは連星パルサーの運動に大きな影響を与え、上記の重力波テンプレート作りの重要な要素となる可能性がある。そこで、本研究では連星パルサーの合体などの相対論的天体力学を念頭に置き、相対論的力学系における非線形現象について詳細に調べ、それが重力波観測計画に与える影響について考察した。その結果、どのような状況で連星パルサーの合体などから放出される重力波において、カオスなどの非線形現象が重要となるのかを明らかにした。また、本研究により、重力系における非線形現象の重要性を明らかにし、相対論的宇宙物理学に相対論的力学系という新しい分野が開拓できたものと思う。

観測されている銀河や銀河団などの宇宙の大構造は現代科学における最も大きな謎の一つである。「COBEなどの観測衛星が明らかにした『凸凹のほとんどない宇宙初期』からいかに『現在の構造』ができたのか？」というのが『宇宙の構造形成問題』である。一番自然なシナリオは，「宇宙初期の密度揺らぎが自己重力で成長し，構造が形成される」とする説であるが，現在の大規模構造を完全に説明するまでに至っていない。この標準的理論の修正版を含めこれまで多くの試みがなされているが，我々は，まったく新しい観点からのアプローチが必要と考える。つまり，宇宙の構造形成問題を物理の基礎的な問題ととらえ，関連する物理的素過程を明らかにしなければその本質が解明されないのではないかと考える。より具体的に述べると，宇宙の構造形成問題を系統的，かつ総合的に研究するには，まずその物理的素過程に立ち戻り，各方面からいろいろな可能性を考え直す必要があると思われる。その際，現在最も必要とされる分野は，揺らぎの起源としての位相欠陥や量子場の揺らぎなどを明らかにする素粒子理論，宇宙の大規模構造を考える際に欠かせない宇宙論や一般相対論，およびその観測的データの提供，さらに自己重力多体系の緩和現象や構造形成問題の新しいアプローチとしてのカオス理論などが考えられるが，早稲田大学にはちょうどこの3分野に第一線で活躍する研究者がおり，特定課題の共同研究を行うにふさわしい状況にあった。そこで，本研究では，次の3つの基礎物理学的観点から構造形成の本質的問題を探り，宇宙の構造形成問題解明に迫った。（1）宇宙初期の相転移・インフレーションを含む素粒子的アプローチ。（2）宇宙の非線形構造形成問題を一般相対論を基礎に考察。（3）自己重力多体系の構造形成問題を非線形物理学，特にカオス理論の観点から考える。 94年度は，まず構造形成問題の基礎過程と考えられる3つの各アプローチに対し，グループに分かれ研究を進めた。素粒子論的観点から量子トンネル現象の基礎的理解およびその宇宙の相転移にともなう位相欠陥，ミニブラックホール形成問題との関連を大場が，また曲がった時空における量子場の振舞いを確率過程量子化の方法を用い金長が，さらにそれに基づきインフレーション宇宙論における密度揺らぎの起源の問題を前田，大場，金長が解析した。また，もう一つの素過程のカオス的アプローチとして，自己重力多体系における構造形成問題を相沢が，より一般的な構造形成問題とカオス理論の関係を宮坂が考察した。その宇宙論へ応用に関しては，前田が加わり検討を行った。第3の宇宙スケールの構造形成に不可欠と考えられる非線形構造形成の一般相対論的アプローチに関しては前田が，また宇宙背景輻射や銀河分布などの現在の構造に関する観測的情報は大師堂が担当した。これらの研究において，大規模なシミュレーション計算は不可欠で，購入したワークステーションおよびスーパーコンピューターを併用し，研究を進めた。また，95年度は，前年度の研究成果を持ち寄り，各アプローチの相互検討を行った。その後はお互いの連絡を密にし，総合的観点から各アプローチを共同で解析し，どの素過程が最も構造形成問題において本質的かつ重要であるかを調べ，宇宙の構造形成問題解明の可能性を探った。